Question

Помогите пожалуйста решить задачу. Не могу разобраться. Сумма двух чисел равна 1 111 110.В разряде сотен большего числа стоит 8 .В тех же разрядах меньшего числа стоит цифра 2.Если заменить эти цифры нулями,то получатся новые числа,одно из которых в 9 раз больше другого.найдите исходные числа.

Answer 1

Ответ:

999 899 и 111 211

Пошаговое объяснение:

В разрядах сотен стоят нужные числа, а сумма соответствует условию. Если заменить эти числа нулями, то получим 999 099 и 111 011, где первое в 9 раз больше второго.

Answer 2

Problem Analysis

To solve this problem, we need to find two numbers whose sum is 1,111,110. The larger number has an 8 in the hundreds place, while the smaller number has a 2 in the same place. If we replace these digits with zeros, the resulting numbers will have a ratio of 9:1. We need to find the original numbers.

Solution

Let's break down the problem step by step:

1. We know that the sum of the two numbers is 1,111,110. Let's call the larger number A and the smaller number B. So, we have the equation A + B = 1,111,110.

2. The larger number has an 8 in the hundreds place, so we can write it as 800 + X, where X represents the remaining digits. Similarly, the smaller number can be written as 200 + Y, where Y represents the remaining digits.

3. If we replace the hundreds digit with zero in both numbers, we get 100X and 100Y. According to the problem, one of these numbers is 9 times larger than the other. So, we have two possible equations: 100X = 9 * 100Y or 100Y = 9 * 100X.

4. Let's solve the first equation: 100X = 9 * 100Y. Dividing both sides by 100, we get X = 9Y.

5. Now, let's substitute the expressions for A and B in terms of X and Y into the equation A + B = 1,111,110. We have (800 + X) + (200 + Y) = 1,111,110. Simplifying, we get 1000 + X + Y = 1,111,110.

6. Substituting X = 9Y from step 4, we have 1000 + 10Y = 1,111,110. Solving for Y, we get Y = 111,110 / 10 - 100.

7. Calculating Y, we find Y = 11,111 - 100 = 11,011.

8. Now that we have Y, we can substitute it back into X = 9Y to find X. X = 9 * 11,011 = 99,099.

9. Finally, we can calculate the original numbers A and B. A = 800 + X = 800 + 99,099 = 99,899, and B = 200 + Y = 200 + 11,011 = 11,211.

Answer

The original numbers are 99,899 and 11,211.

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